CN109840308A - A kind of region wind power probability forecast method and system - Google Patents

A kind of region wind power probability forecast method and system Download PDF

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CN109840308A
CN109840308A CN201711220463.9A CN201711220463A CN109840308A CN 109840308 A CN109840308 A CN 109840308A CN 201711220463 A CN201711220463 A CN 201711220463A CN 109840308 A CN109840308 A CN 109840308A
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CN109840308B (en
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王钊
王伟胜
刘纯
王勃
冯双磊
王铮
姜文玲
赵艳青
车建峰
杨红英
靳双龙
胡菊
马振强
宋宗鹏
王姝
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Shandong Electric Power Co Ltd
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China Electric Power Research Institute Co Ltd CEPRI
State Grid Shandong Electric Power Co Ltd
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Abstract

本发明提供了一种区域风电功率概率预报方法及系统,包括:采集目标时刻风电场的预报功率,从基于预先构建的联合概率分布模型得到的模拟样本集中筛选出符合目标时刻风电场预报功率等级的条件样本集;对所述条件样本集进行拟合得到条件概率分布函数;基于所述条件概率分布函数提取概率预报区间和分位数预报集合。本发明提供的技术方案,根据建立的联合概率分布模型,提取满足风电功率概率预测条件的条件样本集,根据条件样本集构建条件概率分布函数,大大降低了计算难度,提高了工作效率。

The invention provides a method and system for probabilistic forecasting of regional wind power, comprising: collecting the forecast power of a wind farm at a target time, and selecting a forecast power level of the wind farm at the target time from a set of simulated samples obtained based on a pre-built joint probability distribution model The conditional sample set is obtained; a conditional probability distribution function is obtained by fitting the conditional sample set; and a probability prediction interval and a quantile prediction set are extracted based on the conditional probability distribution function. The technical scheme provided by the present invention, according to the established joint probability distribution model, extracts the conditional sample set that meets the wind power probability prediction conditions, and constructs the conditional probability distribution function according to the conditional sample set, which greatly reduces the calculation difficulty and improves the work efficiency.

Description

一种区域风电功率概率预报方法及系统A method and system for probabilistic forecasting of regional wind power

技术领域technical field

本发明属于新能源发电领域,具体涉及一种区域风电功率概率预报方法及系统。The invention belongs to the field of new energy power generation, and in particular relates to a method and system for probabilistic forecasting of regional wind power.

背景技术Background technique

风能资源具有波动性和间歇性的特点导致对其预测的精度有限,因此需要在电力市场和电力调度的决策当中考虑风电变量不确定性分布以得到更加经济合理的结果。因此,能反映功率预报不确定性的概率预报方法得到了广泛的研究。当研究对象是区域多个风电场的预报功率时,高维随机向量中的各个随机变量之间存在着复杂的相关关系,如何精确的拟合这一相关结构关系到了随机向量的多元分布的拟合效果,进而影响到提取的条件概率预报的准确度。The fluctuating and intermittent characteristics of wind energy resources lead to limited prediction accuracy. Therefore, it is necessary to consider the uncertainty distribution of wind power variables in the decision-making of power market and power dispatch to obtain more economical and reasonable results. Therefore, probabilistic forecasting methods that can reflect the uncertainty of power forecasting have been extensively studied. When the research object is the forecast power of multiple wind farms in the region, there is a complex correlation between the random variables in the high-dimensional random vector. How to accurately fit this correlation structure is related to the fitting of the multivariate distribution of the random vector. The combined effect will affect the accuracy of the extracted conditional probability forecast.

传统的相关建模方法采用Gaussian Copula模型进行构建,但是其选用的拟合函数单一,对于复杂相关性的建模精度不足。The traditional correlation modeling method is constructed by Gaussian Copula model, but the fitting function selected is single, and the modeling accuracy of complex correlation is insufficient.

传统的概率预报方法,在进行区域总功率概率预报时,满足目标点条件的样本数量有限,概率预报的效果不佳。The traditional probabilistic forecast method, when carrying out the regional total power probabilistic forecast, has a limited number of samples that meet the conditions of the target point, and the effect of the probabilistic forecast is not good.

发明内容SUMMARY OF THE INVENTION

本发明选择R-vine Copula函数进行相关性建模,提高建模精度,并根据相关性模型得到联合概率分布模型用于风电场功率的概率预报中来,提高工作效率。The invention selects the R-vine Copula function for correlation modeling, improves the modeling accuracy, and obtains a joint probability distribution model according to the correlation model, which is used in the probability prediction of wind farm power to improve work efficiency.

本发明提供的一种区域风电功率概率预报方法,包括:A method for probabilistic forecasting of regional wind power provided by the present invention includes:

采集目标时刻风电场的预报功率;Collect the forecast power of the wind farm at the target time;

从基于预先构建的联合概率分布模型得到的模拟样本集中筛选出符合目标时刻风电场预报功率等级的条件样本集;From the simulated sample set based on the pre-built joint probability distribution model, select the conditional sample set that meets the forecast power level of the wind farm at the target time;

对所述条件样本集进行拟合得到条件概率分布函数;Fitting the conditional sample set to obtain a conditional probability distribution function;

基于所述条件概率分布函数提取概率预报区间和分位数预报集合。Probability forecast intervals and quantile forecast sets are extracted based on the conditional probability distribution function.

所述联合概率分布模型的构建,包括:The construction of the joint probability distribution model includes:

基于风电场的历史数据,构建随机向量;Build a random vector based on the historical data of the wind farm;

对随机向量的随机变量进行边缘分布拟合,得到边缘累积分布函数;Perform marginal distribution fitting on the random variables of the random vector to obtain the marginal cumulative distribution function;

根据边缘累积分布函数和随机向量得到相关性向量;Obtain the correlation vector according to the marginal cumulative distribution function and the random vector;

根据相关性向量,确定R-vine copula模型;According to the correlation vector, determine the R-vine copula model;

根据R-vine copula模型和各随机变量的边缘累积分布函数得到的联合概率分布模型;The joint probability distribution model obtained according to the R-vine copula model and the marginal cumulative distribution function of each random variable;

所述历史数据包括:历史预报功率和历史预报误差。The historical data includes: historical forecast power and historical forecast error.

所述基于风电场的历史数据,构建随机向量,包括:The random vector is constructed based on the historical data of the wind farm, including:

以所述历史数据中的同一时刻的数据为一行构建包括t个时刻数据的矩阵,将所述矩阵用随机向量表示。A matrix including data at t moments is constructed by taking the data at the same time in the historical data as a row, and the matrix is represented by a random vector.

所述根据相关性向量,确定R-vine copula模型,包括:The R-vine copula model is determined according to the correlation vector, including:

计算相关性向量中两两变量间的Kendall秩相关系数;Calculate the Kendall rank correlation coefficient between the two variables in the correlation vector;

选择满足Kendall秩相关系数总和最大化生成树结构;Choose a spanning tree structure that maximizes the sum of Kendall rank correlation coefficients;

为生成树中每个边确定二元copula函数并进行参数估计。Determine a binary copula function and perform parameter estimation for each edge in the spanning tree.

所述基于预先构建的联合概率分布模型得到模拟样本集,包括:The simulated sample set obtained based on the pre-built joint probability distribution model includes:

任意生成满足均匀分布的独立随机向量;Arbitrarily generate independent random vectors that satisfy uniform distribution;

根据所述独立随机向量结合所述R-vine Copula模型生成相关性的随机向量;Generate a random vector of correlation according to the independent random vector in combination with the R-vine Copula model;

根据边缘累积分布函数的反函数,从相关性的随机向量求得目标随机向量,以所述目标随机向量为模拟样本集。According to the inverse function of the marginal cumulative distribution function, the target random vector is obtained from the random vector of the correlation, and the target random vector is used as a simulated sample set.

对所述条件样本集进行拟合、以及对所述随机向量的随机变量进行边缘分布拟合均采用核密度估计的方法。Both the fitting of the conditional sample set and the marginal distribution fitting of the random variable of the random vector use the method of kernel density estimation.

本发明提供的一种区域风电功率概率预报系统,包括:A regional wind power probabilistic forecast system provided by the present invention includes:

模型构建模块,用于预先构建联合概率分布模型;A model building module for pre-constructing a joint probability distribution model;

采集模块,用于采集目标时刻的风电场的预报功率;The acquisition module is used to collect the forecast power of the wind farm at the target time;

条件样本模块,用于从基于预先构建的联合概率分布模型得到的模拟样本集中筛选出符合目标时刻风电场预报功率的条件样本集;The conditional sample module is used to select the conditional sample set that meets the forecast power of the wind farm at the target time from the simulated sample set obtained based on the pre-built joint probability distribution model;

拟合模块,用于对所述条件样本集进行拟合得到条件概率分布函数;a fitting module for fitting the conditional sample set to obtain a conditional probability distribution function;

预报模块,用于基于所述条件概率分布函数提取概率预报区间和分位数预报集合。A forecasting module, configured to extract a probability forecast interval and a quantile forecast set based on the conditional probability distribution function.

所述模型构建模块,包括:The model building module includes:

随机向量单元,用于基于风电场的历史数据,构建随机向量;The random vector unit is used to construct a random vector based on the historical data of the wind farm;

边缘分布拟合单元,用于对随机向量的随机变量进行边缘分布拟合,得到边缘累积分布函数;The marginal distribution fitting unit is used to perform marginal distribution fitting on the random variables of the random vector to obtain the marginal cumulative distribution function;

相关性向量单元,用于根据边缘累积分布函数和随机向量得到相关性向量;The correlation vector unit is used to obtain the correlation vector according to the edge cumulative distribution function and the random vector;

R-vine copula模型单元,用于根据相关性向量,确定R-vine copula模型;The R-vine copula model unit is used to determine the R-vine copula model according to the correlation vector;

联合概率分布模型单元,用于根据R-vine copula模型和各随机变量的边缘累积分布函数得到的联合概率分布模型;The joint probability distribution model unit is used for the joint probability distribution model obtained according to the R-vine copula model and the marginal cumulative distribution function of each random variable;

所述历史数据包括:历史预报功率和历史预报误差。The historical data includes: historical forecast power and historical forecast error.

所述条件样本模块,包括:The conditional sample module includes:

第一生成单元,用于任意生成满足均匀分布的独立随机向量;The first generating unit is used to arbitrarily generate independent random vectors satisfying uniform distribution;

第二生成单元,用于根据所述独立随机向量结合R-vine Copula模型生成相关性的随机向量;a second generating unit, configured to generate a random vector of correlation according to the independent random vector in combination with the R-vine Copula model;

样本确定单元,用于根据边缘累积分布函数的反函数,从相关性的随机向量求得目标随机向量,以所述目标随机向量为模拟样本集;a sample determination unit, configured to obtain a target random vector from the random vector of the correlation according to the inverse function of the edge cumulative distribution function, and use the target random vector as a simulated sample set;

筛选单元,用于从所述模拟样本集中筛选出符合目标时刻风电场预报功率的条件样本集。The screening unit is used for screening out the conditional sample set that meets the forecast power of the wind farm at the target time from the simulation sample set.

所述R-vine copula模型单元,包括:The R-vine copula model unit includes:

系数计算子单元,用于计算相关性向量中两两变量间的Kendall秩相关系数;The coefficient calculation subunit is used to calculate the Kendall rank correlation coefficient between the two variables in the correlation vector;

生成树子单元,用于选择满足Kendall秩相关系数总和最大化生成树结构;The spanning tree subunit is used to select a spanning tree structure that maximizes the sum of Kendall rank correlation coefficients;

模型确定子单元,用于为生成树中每个边确定二元copula函数并进行参数估计。The model determination subunit is used to determine the binary copula function and perform parameter estimation for each edge in the spanning tree.

与最接近的现有技术比,本发明提供的技术方案具有以下有益效果:Compared with the closest prior art, the technical solution provided by the present invention has the following beneficial effects:

本发明提供的技术方案,根据建立联合概率分布模型,提取满足风电功率概率预测条件的条件样本集,根据条件样本集构建条件概率分布函数,大大降低了计算难度,提高了工作效率;According to the technical scheme provided by the present invention, according to the establishment of a joint probability distribution model, a conditional sample set that satisfies the probability prediction conditions of wind power power is extracted, and a conditional probability distribution function is constructed according to the conditional sample set, which greatly reduces the calculation difficulty and improves the work efficiency;

本发明提供的技术方案,采用R-vine Copula函数可以实现高维相关结构的拆分以及多种二元Copula函数的选取拟合,从而提高相关性建模的灵活性和精确度。In the technical scheme provided by the present invention, the R-vine Copula function can be used to realize the splitting of high-dimensional correlation structures and the selection and fitting of various binary Copula functions, thereby improving the flexibility and accuracy of correlation modeling.

附图说明Description of drawings

图1为本发明一种区域风电功率概率预报方法流程图;1 is a flow chart of a method for probabilistic forecasting of regional wind power according to the present invention;

图2为本发明实施例一种区域风电功率概率预报方法整体流程图。2 is an overall flow chart of a method for probabilistic forecasting of regional wind power according to an embodiment of the present invention.

具体实施方式Detailed ways

下面结合附图对本发明做进一步详细的说明:Below in conjunction with accompanying drawing, the present invention is described in further detail:

实施例一:Example 1:

图1为本发明一种区域风电功率概率预报方法流程图,如图1所示,本发明提供的一种区域风电功率概率预报方法,可以包括:Fig. 1 is a flow chart of a method for probabilistic forecasting of regional wind power according to the present invention. As shown in Fig. 1, a method for probabilistic forecasting of regional wind power provided by the present invention may include:

采集目标时刻风电场的预报功率;Collect the forecast power of the wind farm at the target time;

从基于预先构建的联合概率分布模型得到的模拟样本集中筛选出符合目标时刻风电场预报功率等级的条件样本集;From the simulated sample set based on the pre-built joint probability distribution model, select the conditional sample set that meets the forecast power level of the wind farm at the target time;

对所述条件样本集进行拟合得到条件概率分布函数;Fitting the conditional sample set to obtain a conditional probability distribution function;

基于所述条件概率分布函数提取概率预报区间和分位数预报集合。Probability forecast intervals and quantile forecast sets are extracted based on the conditional probability distribution function.

所述联合概率分布模型的构建,包括:The construction of the joint probability distribution model includes:

基于风电场的历史数据,构建随机向量;Build a random vector based on the historical data of the wind farm;

对随机向量的随机变量进行边缘分布拟合,得到边缘累积分布函数;Perform marginal distribution fitting on the random variables of the random vector to obtain the marginal cumulative distribution function;

根据边缘累积分布函数和随机向量得到相关性向量;Obtain the correlation vector according to the marginal cumulative distribution function and the random vector;

根据相关性向量,确定R-vine copula模型;According to the correlation vector, determine the R-vine copula model;

根据R-vine copula模型和各随机变量的边缘累积分布函数得到的联合概率分布模型;The joint probability distribution model obtained according to the R-vine copula model and the marginal cumulative distribution function of each random variable;

所述历史数据包括:历史预报功率和历史预报误差。The historical data includes: historical forecast power and historical forecast error.

所述基于风电场的历史数据,构建随机向量,包括:The random vector is constructed based on the historical data of the wind farm, including:

以所述历史数据中的同一时刻的数据为一行构建包括t个时刻数据的矩阵,将所述矩阵用随机向量表示。A matrix including data at t moments is constructed by taking the data at the same time in the historical data as a row, and the matrix is represented by a random vector.

所述根据相关性向量,确定R-vine copula模型,包括:The R-vine copula model is determined according to the correlation vector, including:

计算相关性向量中两两变量间的Kendall秩相关系数;Calculate the Kendall rank correlation coefficient between the two variables in the correlation vector;

选择满足Kendall秩相关系数总和最大化生成树结构;Choose a spanning tree structure that maximizes the sum of Kendall rank correlation coefficients;

为生成树中每个边确定二元copula函数并进行参数估计。Determine a binary copula function and perform parameter estimation for each edge in the spanning tree.

所述基于预先构建的联合概率分布模型得到模拟样本集,包括:The simulated sample set obtained based on the pre-built joint probability distribution model includes:

任意生成一个满足均匀分布的独立随机向量;Arbitrarily generate an independent random vector that satisfies a uniform distribution;

根据所述独立随机向量结合所述R-vine Copula模型生成相关性的随机向量;Generate a random vector of correlation according to the independent random vector in combination with the R-vine Copula model;

根据边缘累积分布函数的反函数,从相关性的随机向量求得目标随机向量,以所述目标随机向量为模拟样本集。According to the inverse function of the marginal cumulative distribution function, the target random vector is obtained from the random vector of the correlation, and the target random vector is used as a simulated sample set.

对所述条件样本集进行拟合、以及对所述随机向量的随机变量进行边缘分布拟合均采用核密度估计的方法。Both the fitting of the conditional sample set and the marginal distribution fitting of the random variable of the random vector use the method of kernel density estimation.

实施例二:Embodiment 2:

基于相同的发明构思,本发明提供的一种区域风电功率概率预报系统,可以包括:Based on the same inventive concept, a regional wind power probabilistic forecast system provided by the present invention may include:

模型构建模块,用于预先构建联合概率分布模型;A model building module for pre-constructing a joint probability distribution model;

采集模块,用于采集目标时刻的风电场的预报功率;The acquisition module is used to collect the forecast power of the wind farm at the target time;

条件样本模块,用于从基于预先构建的联合概率分布模型得到的模拟样本集中筛选出符合目标时刻风电场预报功率的条件样本集;The conditional sample module is used to select the conditional sample set that meets the forecast power of the wind farm at the target time from the simulated sample set obtained based on the pre-built joint probability distribution model;

拟合模块,用于对所述条件样本集进行拟合得到条件概率分布函数;a fitting module for fitting the conditional sample set to obtain a conditional probability distribution function;

预报模块,用于基于所述条件概率分布函数提取概率预报区间和分位数预报集合。A forecasting module, configured to extract a probability forecast interval and a quantile forecast set based on the conditional probability distribution function.

所述模型构建模块,包括:The model building module includes:

随机向量单元,用于基于风电场的历史数据,构建随机向量;The random vector unit is used to construct a random vector based on the historical data of the wind farm;

边缘分布拟合单元,用于对随机向量的随机变量进行边缘分布拟合,得到边缘累积分布函数;The marginal distribution fitting unit is used to perform marginal distribution fitting on the random variables of the random vector to obtain the marginal cumulative distribution function;

相关性向量单元,用于根据边缘累积分布函数和随机向量得到相关性向量;The correlation vector unit is used to obtain the correlation vector according to the edge cumulative distribution function and the random vector;

R-vine copula模型单元,用于根据相关性向量,确定R-vine copula模型;The R-vine copula model unit is used to determine the R-vine copula model according to the correlation vector;

联合概率分布模型单元,用于根据R-vine copula模型和各随机变量的边缘累积分布函数得到的联合概率分布模型;The joint probability distribution model unit is used for the joint probability distribution model obtained according to the R-vine copula model and the marginal cumulative distribution function of each random variable;

所述历史数据包括:历史预报功率和历史预报误差。The historical data includes: historical forecast power and historical forecast error.

所述条件样本模块,包括:The conditional sample module includes:

第一生成单元,用于任意生成满足均匀分布的独立随机向量;The first generating unit is used to arbitrarily generate independent random vectors satisfying uniform distribution;

第二生成单元,用于根据所述独立随机向量结合R-vine Copula模型生成相关性的随机向量;a second generating unit, configured to generate a random vector of correlation according to the independent random vector in combination with the R-vine Copula model;

样本确定单元,用于根据边缘累积分布函数的反函数,从相关性的随机向量求得目标随机向量,以所述目标随机向量为模拟样本集;a sample determination unit, configured to obtain a target random vector from the random vector of the correlation according to the inverse function of the edge cumulative distribution function, and use the target random vector as a simulated sample set;

筛选单元,用于从所述模拟样本集中筛选出符合目标时刻风电场预报功率的条件样本集。The screening unit is used for screening out the conditional sample set that meets the forecast power of the wind farm at the target time from the simulation sample set.

所述R-vine copula模型单元,包括:The R-vine copula model unit includes:

系数计算子单元,用于计算相关性向量中两两变量间的Kendall秩相关系数;The coefficient calculation subunit is used to calculate the Kendall rank correlation coefficient between the two variables in the correlation vector;

生成树子单元,用于选择满足Kendall秩相关系数总和最大化生成树结构;The spanning tree subunit is used to select a spanning tree structure that maximizes the sum of Kendall rank correlation coefficients;

模型确定子单元,用于为生成树中每个边确定二元copula函数并进行参数估计。The model determination subunit is used to determine the binary copula function and perform parameter estimation for each edge in the spanning tree.

所述随机向量单元包括:The random vector unit includes:

以同一时刻的数据为一行构建包括t个时刻数据的矩阵,将所述矩阵用随机向量表示。A matrix including data at t moments is constructed with the data at the same time as a row, and the matrix is represented by a random vector.

实施例三:Embodiment three:

一种区域风电功率概率预报方法,可以包括:A method for probabilistic forecasting of regional wind power, which can include:

构建R-vine copula模型和基于R-vine copula模型进行风电功率概率预报;Build an R-vine copula model and make probabilistic forecast of wind power based on the R-vine copula model;

图2为一种区域风电功率概率预报方法整体流程图,如图2所示,所述构建R-vinecopula模型,可以包括:Figure 2 is an overall flow chart of a method for probabilistic forecasting of regional wind power. As shown in Figure 2, the construction of the R-vinecopula model may include:

步骤1-1:输入d维样本[X1,...,Xd]=[P1,...,Pn,E1,...,En];Step 1-1: Input d-dimensional samples [X 1 ,...,X d ]=[P 1 ,...,P n ,E 1 ,...,E n ];

步骤1-2:对样本中的元素进行边缘拟合得到拟合的边缘累积分布函数;Step 1-2: Perform edge fitting on the elements in the sample to obtain the fitted edge cumulative distribution function;

步骤1-3:去除[X1,...,Xd]中边缘分布的影响得到d维样本数据[U1,…,Ud];Step 1-3: remove the influence of marginal distribution in [X 1 ,...,X d ] to obtain d-dimensional sample data [U 1 ,...,U d ];

步骤1-4:基于d维样本数据[U1,…,Ud],根据相关系数最大化原则筛选出最大生成树,并得到树中的相关变量对;检验相关变量对是否独立,是则判断所有树是否都生成了,否则筛选出树需要的二元Copula函数并进行参数估计后判断所有树是否都生成了,若所有树都生成,则R-vine copula模型构建完成,若未完成所有树的生成则重复此步骤,直至所有树都生成。Step 1-4: Based on the d-dimensional sample data [U 1 ,...,U d ], filter out the maximum spanning tree according to the principle of maximizing the correlation coefficient, and obtain the relevant variable pairs in the tree; check whether the relevant variable pairs are independent, if yes Determine whether all trees have been generated, otherwise filter out the binary copula function required by the tree and perform parameter estimation to determine whether all trees have been generated. If all trees are generated, the R-vine copula model construction is completed. For tree generation, repeat this step until all trees are generated.

在所有树都生成之后,可以基于R-vine copula模型进行风电功率概率预报步骤,其中,所述基于R-vine copula模型进行风电功率概率预报,可以包括:After all trees are generated, the step of probabilistic forecasting of wind power based on the R-vine copula model may be performed, wherein the probabilistic forecast of wind power based on the R-vine copula model may include:

步骤2-1:基于R-vine copula模型,通过随机采样的方法得到模拟样本集S;Step 2-1: Based on the R-vine copula model, obtain the simulated sample set S by random sampling;

步骤2-2:根据概率预报条件在S中筛选符合预报目标点的样本;Step 2-2: According to the probability forecast conditions, select the samples that meet the forecast target points in S;

步骤2-3:对筛选出的样本进行条件概率密度分布拟合,输出条件概率密度函数。Step 2-3: Perform conditional probability density distribution fitting on the selected samples, and output the conditional probability density function.

具体的:specific:

步骤1-1:输入d维样本[X1,...,Xd]=[P1,...,Pn,E1,...,En]中的d维样本的生成可以包括:Step 1-1: The generation of the d-dimensional samples in the input d-dimensional samples [X 1 ,...,X d ]=[P 1 ,...,P n ,E 1 ,...,E n ] can be include:

需要建模的对象是区域内各个风电场的预报功率p以及预报误差e,(5-1)给出了n个风电场的示例,其中矩阵中每一行对应同一时间的数据,根据样本集大小共有t个时刻的数据,每一列对应的随机变量由大写的P和E表示,为了表述方便统一表示为d维的随机向量X=(X1,…,Xd)。The objects that need to be modeled are the forecast power p and forecast error e of each wind farm in the region. (5-1) gives an example of n wind farms, where each row in the matrix corresponds to the data at the same time, according to the size of the sample set There are a total of t time data, and the random variables corresponding to each column are represented by uppercase P and E, which are uniformly represented as a d-dimensional random vector X=(X 1 ,...,X d ) for the convenience of expression.

步骤1-2:对样本中的元素进行边缘拟合得到拟合的边缘分布模型,可以包括:Step 1-2: Perform edge fitting on the elements in the sample to obtain a fitted edge distribution model, which may include:

考虑到各边缘变量难以确定一个统一的参数分布且经验分布函数是非连续的,本方法采用核密度估计的非参数分布进行边缘分布的拟合,拟合的概率密度函数如式(5-2)所示。Considering that it is difficult to determine a uniform parametric distribution for each marginal variable and the empirical distribution function is discontinuous, this method uses the non-parametric distribution of kernel density estimation to fit the marginal distribution, and the fitted probability density function is shown in Equation (5-2) shown.

其中,h为带宽,K表示核函数,此处本发明采用高斯核,表达式如式(5-3)所示,n表示样本量,X表示样本数据。Among them, h is the bandwidth, K represents the kernel function, and the present invention uses a Gaussian kernel, and the expression is shown in formula (5-3), n represents the sample size, and X represents the sample data.

步骤1-3:去除[X1,...,Xd]中边缘分布的影响得到d维样本数据[U1,…,Ud],可以包括:Step 1-3: Remove the influence of marginal distribution in [X 1 ,...,X d ] to obtain d-dimensional sample data [U 1 ,...,U d ], which can include:

相应的根据估计的边缘累积分布函数和X可以得到剥离了边缘分布影响的相关性向量U=(U1,...,Ud),其对应的边缘分布满足均匀分布。The corresponding marginal cumulative distribution function according to the estimate and X can obtain the correlation vector U=(U 1 , . . . , U d ) stripped of the influence of the edge distribution, and the corresponding edge distribution satisfies the uniform distribution.

通过边缘累积分布函数将X转化为U,剥离边缘分布的影响,仅考虑相关结构如式Convert X to U through the edge cumulative distribution function, strip the influence of the edge distribution, and only consider the relevant structure such as Eq.

其中,是边缘累积分布函数CDF的反函数,U=(U1,...,Ud)∈[0,1]din, is the inverse function of the marginal cumulative distribution function CDF, U=(U 1 ,...,U d )∈[0,1] d .

步骤1-4:基于d维样本数据[U1,…,Ud],根据相关系数最大化原则筛选出最大生成树,并得到树中的相关变量对,检验相关变量对是否独立,是则判断所有树是否都生成了,否则筛选出树需要的二元Copula函数并进行参数估计后判断所有树是否都生成了,若所有树都生成,则R-vine copula模型构建完成,若未完成所有树的生成则重复此步骤,直至所有树都生成,可以包括:Step 1-4: Based on the d-dimensional sample data [U 1 ,...,U d ], screen out the maximum spanning tree according to the principle of maximizing the correlation coefficient, and obtain the relevant variable pairs in the tree, and test whether the relevant variable pairs are independent, if yes, then Determine whether all trees have been generated, otherwise filter out the binary copula function required by the tree and perform parameter estimation to determine whether all trees have been generated. If all trees are generated, the R-vine copula model construction is completed. For tree generation, this step is repeated until all trees are generated, which can include:

根据上一步中得到的U,确定相应的R-vine copula需要完成以下三项工作:According to the U obtained in the previous step, determining the corresponding R-vine copula requires the following three tasks:

1.选择R-vine结构,即给出各树的约束条件集合{j(e),k(e)D(e)}。1. Select the R-vine structure, that is, give the set of constraints {j(e), k(e)D(e)} for each tree.

2.给R-vine中每个边e对应的二元随机变量选择合适的二元copula类型。2. Select a suitable binary copula type for the binary random variable corresponding to each edge e in R-vine.

3.估计各二元copula函数的参数。3. Estimate the parameters of each binary copula function.

以上三项在实际应用中常常是结合在一起进行的,根据逐次法来逐棵树的实现对R-vine copula的构建。其算法流程如下:The above three items are often combined in practical applications, and the construction of R-vine copula is implemented tree by tree according to the successive method. The algorithm flow is as follows:

基于模型计算成本的考虑,在进行二元Copula拟合和参数估计之前,引入独立性检验,对于接近独立的随机变量对则直接采用独立的copula函数,根据显著程度的大小控制对应模型的计算复杂度和精确度。Based on the consideration of the computational cost of the model, an independence test is introduced before binary copula fitting and parameter estimation. For pairs of random variables that are close to independent, an independent copula function is directly used to control the computational complexity of the corresponding model according to the degree of significance. degree and precision.

具体的,基于R-vine copula模型进行风电功率概率预报可以包括:Specifically, the probabilistic forecast of wind power based on the R-vine copula model may include:

根据R-vine copula模型得到联合概率分布函数,联合概率分布函数虽然是连续解析的数学表达式,然而,在进行区域总功率概率预报时,计算的对象需要经过多重积分计算得到,而在积分函数复杂的情况下进行积分计算难度很大,不具备工程实用意义,因此,考虑根据所得的联合概率分布函数生成足够数量的数据样本来拟合出满足条件的条件概率密度结果。According to the R-vine copula model, the joint probability distribution function is obtained. Although the joint probability distribution function is a mathematical expression of continuous analysis, when the regional total power probability forecast is performed, the calculated object needs to be calculated by multiple integrals, and in the integral function In complex cases, it is very difficult to perform integral calculation and has no practical significance in engineering. Therefore, it is considered to generate a sufficient number of data samples according to the obtained joint probability distribution function to fit the conditional probability density results that meet the conditions.

首先,由计算机任意生成一个满足均匀分布U(0,1)d的d维独立随机向量W:=(W1,...,Wd)。First, a d-dimensional independent random vector W:=(W 1 ,...,W d ) satisfying the uniform distribution U(0,1) d is randomly generated by the computer.

然后通过(5-4)生成相关性的随机向量 Then generate a random vector of correlations by (5-4)

最后,根据拟合的各边缘累计分布函数的反函数,即求得目标随机向量在获得足够数量模拟样本(模拟样本集S)的情况下,认为包含了联合分布的全部信息,本发明根据区域内各风电场预报功率等级为条件筛选出符合条件的区域总功率的样本点,组成集合C,然后对C中的样本采用核密度估计的方法(同公式5-1)构建连续的概率分布函数,并根据实际需求提取不同置信度的预报区间结果。Finally, according to the inverse function of the fitted edge cumulative distribution function, namely from Find the target random vector After obtaining a sufficient number of simulated samples (simulation sample set S), it is considered that Contains all the information of the joint distribution, the present invention selects the sample points of the total power of the region that meet the conditions according to the forecast power level of each wind farm in the region, and forms a set C, and then adopts the method of kernel density estimation for the samples in C ( The same formula 5-1) builds a continuous probability distribution function, and extracts forecast interval results with different confidence levels according to actual needs.

根据R-vine copula模型得到联合概率分布函数,可以包括:The joint probability distribution function is obtained according to the R-vine copula model, which can include:

规则藤(Regular vine,R-vine)V是d个元素的规则藤,它的边的集合表示为E(V)=E1∪…∪Ei∪…∪Ed-1,其中Ei,i=1,…,d-1代表了第i棵树Ti的边的集合。规则藤需要满足以下三个条件:Regular vine (Regular vine, R-vine) V is a regular vine of d elements, and the set of its edges is expressed as E(V)=E 1 ∪…∪E i ∪…∪E d-1 , where E i , i=1,...,d-1 represents the set of edges of the i-th tree T i . Rule vines need to meet the following three conditions:

4)V={T1,…,Td-1},即d-1个树构成的集合。4) V={T 1 ,...,T d-1 }, that is, a set composed of d-1 trees.

5)T1的节点集合为N1={1,…,d},边集合为E1;而对于i=2,…,d-1,Ti的节点集合为Ni,边集合为Ei,需要满足条件Ni=Ei-15) The node set of T 1 is N 1 ={1,...,d}, and the edge set is E 1 ; and for i=2,...,d-1, the node set of T i is N i , and the edge set is E i , the condition Ni =E i -1 needs to be satisfied.

6)(邻近原则)对于i=2,…,d-1,{a,b}∈Ei,#(a△b)=2,其中△表示计算集合的对等差分,#表示计算集合的势。6) (Proximity principle) For i=2,...,d-1, {a,b}∈E i , #(a△b)=2, where △ represents the equivalent difference of the calculation set, # represents the calculation set potential.

7)维度为d的规则藤V由d-1棵树{T1,…,Td-1}构成,其节点集合为{N1,…,Nd-1},其中集合N1={1,…,d},在相关性建模中对应初始的d个随机变量的编号。V的边集合表示为{E1,…,Ed-1},树Ti的边集合Ei中的一个边e可以表示为e=j(e),k(e)|D(e)的形式,其中{j(e),k(e),j(e)≠k(e)}称为conditioned集合,而D(e)称为conditioning集合,这两个集合中的元素由{1,…,d}构成。根据邻近原则,e由Ei-1中对应的两个边a=j(a),k(a)|D(a),b=j(b),k(b)|D(b)决定,a和b在Ti-1中有一个公共的节点,则三个边的关系就表述成了如下两个关系7) The regular vine V with dimension d is composed of d-1 trees {T 1 ,...,T d-1 }, and its node set is {N 1 ,...,N d-1 }, where the set N 1 ={ 1,...,d}, the number corresponding to the initial d random variables in the correlation modeling. The edge set of V is represented as {E 1 ,...,E d-1 }, and an edge e in the edge set E i of the tree T i can be represented as e=j(e),k(e)|D(e) The form of , where {j(e), k(e), j(e)≠k(e)} is called the conditioned set, and D(e) is called the conditioning set, and the elements in these two sets are represented by {1 ,…,d} constitutes. According to the principle of proximity, e is determined by the corresponding two edges a=j(a), k(a)|D(a), b=j(b), k(b)|D(b) in E i-1 , a and b have a common node in T i-1 , then the relationship of the three edges is expressed as the following two relationships

D(e):=U(a)∩U(b) (3-4)D(e):=U(a)∩U(b) (3-4)

{j(e),k(e)}:=U(a)∪U(b)\D(e), (3-5){j(e),k(e)}:=U(a)∪U(b)\D(e), (3-5)

其中,U(e):={j(e),k(e),D(e)}表示e所含元素的全集,囊括了conditioning集合和conditioned集合中的所有元素。此外,对于E1中的边来说,其形式为e=j(e),k(e),因为此时的conditioning集合D(e)是空集。Among them, U(e):={j(e), k(e), D(e)} represents the complete set of elements contained in e, including all elements in the conditioning set and the conditioned set. In addition, for the edge in E1, its form is e = j(e), k(e), because the conditioning set D(e) at this time is an empty set.

当边的标记规则明确后,则e对应的二元copula密度就可以表示为cj(e),k(e)|D(e)When the edge labeling rules are clarified, the binary copula density corresponding to e can be expressed as c j(e),k(e)|D(e) .

结合上述内容,给出规则藤结构描述的多维联合密度分布的公式:Combined with the above content, the formula of the multi-dimensional joint density distribution described by the regular vine structure is given:

其对应d维随机变量X:=(X1,...,Xd),边缘累积分布函数为fk,k=1,...,d,XD(e)表示X由D(e)规定的子集。其中,公式里第i棵树中的某一个二元copula中的变量——条件分布函数F(xj(e)|xD(e))和F(xk(e)|xD(e))可以通过第i-1棵树中已经估计好参数的copula函数C和相应的条件分布函数F计算得到。Its corresponding d-dimensional random variable X:=(X 1 ,...,X d ), the marginal cumulative distribution function is f k , k=1,...,d, X D(e) represents X by D(e ) specified subset. Among them, the variables in a binary copula in the ith tree in the formula - conditional distribution functions F(x j(e) |x D(e) ) and F(x k(e) |x D(e ) ) can be calculated by the copula function C and the corresponding conditional distribution function F in the i-1th tree whose parameters have been estimated.

本领域内的技术人员应明白,本申请的实施例可提供为方法、系统、或计算机程序产品。因此,本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且,本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器,使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中,使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品,该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flow of the flowcharts and/or the block or blocks of the block diagrams.

这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上,使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理,从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

最后应当说明的是:以上实施例仅用于说明本发明的技术方案而非对其保护范围的限制,尽管参照上述实施例对本申请进行了详细的说明,所属领域的普通技术人员应当理解:本领域技术人员阅读本申请后依然可对申请的具体实施方式进行种种变更、修改或者等同替换,但这些变更、修改或者等同替换,均在申请待批的权利要求保护范围之内。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its protection scope. Although the application has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: After reading this application, those skilled in the art can still make various changes, modifications or equivalent replacements to the specific embodiments of the application, but these changes, modifications or equivalent replacements are all within the protection scope of the pending claims.

Claims (10)

1. A regional wind power probability forecasting method is characterized by comprising the following steps:
acquiring forecast power of a wind power plant at a target moment;
screening out a condition sample set which accords with the forecast power level of the wind power plant at a target moment from a simulation sample set obtained based on a pre-constructed joint probability distribution model;
fitting the conditional sample set to obtain a conditional probability distribution function;
and extracting a probability forecast interval and a quantile forecast set based on the conditional probability distribution function.
2. The regional wind power probability forecasting method of claim 1, wherein the building of the joint probability distribution model comprises:
constructing a random vector based on historical data of the wind power plant;
performing edge distribution fitting on random variables of the random vectors to obtain an edge cumulative distribution function;
obtaining a correlation vector according to the edge cumulative distribution function and the random vector;
determining an R-vine copula model according to the relevance vector;
obtaining a joint probability distribution model according to the R-vine copula model and the edge cumulative distribution function of each random variable;
the historical data includes: historical forecast power and historical forecast error.
3. The regional wind power probability forecasting method of claim 2, characterized in that the construction of the random vector based on the historical data of the wind farm comprises:
and constructing a matrix comprising t time data by taking the data at the same time in the historical data as a row, and representing the matrix by using a random vector.
4. The regional wind power probability forecasting method of claim 2, wherein the determining an R-vine copula model according to the relevance vector comprises:
calculating Kendall rank correlation coefficients between every two variables in the correlation vector;
selecting a spanning tree structure which meets the Kendall rank correlation coefficient sum maximization;
a binary copula function is determined for each edge in the spanning tree and parameter estimation is performed.
5. The regional wind power probability forecasting method of claim 2, wherein the obtaining of the simulation sample set based on the pre-constructed joint probability distribution model comprises:
generating independent random vectors meeting the uniform distribution at will;
generating a random vector of correlation according to the independent random vector and the R-vine Copula model;
and obtaining a target random vector from the random vector of the correlation according to the inverse function of the edge cumulative distribution function, and taking the target random vector as a simulation sample set.
6. The regional wind power probability forecasting method of claim 2, characterized in that fitting the condition sample set and fitting the edge distribution of the random variables of the random vector both adopt a kernel density estimation method.
7. A regional wind power probability forecasting system is characterized by comprising:
the model construction module is used for constructing a joint probability distribution model in advance;
the collection module is used for collecting the forecast power of the wind power plant at a target moment;
the system comprises a conditional sample module, a power source module and a power source module, wherein the conditional sample module is used for screening out a conditional sample set which accords with the forecast power of a wind power plant at a target moment from a simulated sample set obtained based on a pre-constructed joint probability distribution model;
the fitting module is used for fitting the conditional sample set to obtain a conditional probability distribution function;
and the forecasting module is used for extracting a probability forecasting interval and a quantile forecasting set based on the conditional probability distribution function.
8. The regional wind power probability forecasting system of claim 7, wherein the model building module comprises:
the random vector unit is used for constructing a random vector based on historical data of the wind power plant;
the edge distribution fitting unit is used for performing edge distribution fitting on the random variable of the random vector to obtain an edge cumulative distribution function;
the correlation vector unit is used for obtaining a correlation vector according to the edge cumulative distribution function and the random vector;
the R-vine copula model unit is used for determining an R-vine copula model according to the relevance vector;
the joint probability distribution model unit is used for obtaining a joint probability distribution model according to the R-vine copula model and the edge cumulative distribution function of each random variable;
the historical data includes: historical forecast power and historical forecast error.
9. The regional wind power probability forecasting system of claim 8, wherein the condition sample module comprises:
a first generating unit for arbitrarily generating independent random vectors satisfying uniform distribution;
the second generation unit is used for generating a random vector of correlation according to the independent random vector and an R-vine Copula model;
the sample determining unit is used for obtaining a target random vector from the random vector of the correlation according to an inverse function of the edge cumulative distribution function, and the target random vector is taken as a simulation sample set;
and the screening unit is used for screening out a condition sample set which accords with the forecast power of the wind power plant at the target moment from the simulation sample set.
10. The regional wind power probability forecasting system of claim 8, wherein the R-vine copula model unit comprises:
the coefficient calculating subunit is used for calculating Kendall rank correlation coefficients between every two variables in the correlation vector;
the spanning tree subunit is used for selecting a spanning tree structure which meets the Kendall rank correlation coefficient sum maximization;
and the model determining subunit is used for determining a binary copula function for each edge in the spanning tree and performing parameter estimation.
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